Rationality problem for fields of invariants
| Project/Area Number |
25400027
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Niigata University |
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Principal Investigator |
Hoshi Akinari 新潟大学, 自然科学系, 准教授 (50434262)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 有理性問題 / ネーター問題 / 不分岐ブラウアー群 / 不分岐コホモロジー / 双有理分類 / 半単項式作用 / 安定有理性 / レトラクト有理性 / 不分岐コホモロジー群 / relation module / ガロア逆問題 |
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| Outline of Final Research Achievements |
In view of constructive inverse Galois problem, we studied the rationality problem for fields of invariants under the action of finite groups. The invariant called the unramified Brauer group, which is important for the study of the rationality problem, was completely determined when the order of the group is the fifth power of odd prime p. Even for the unramified cohomology group which is a generalization of the unramified Brauer group, we showed that the non-vanishing of it when the order of the group is the ninth power of odd prime p. We studied Noether's problem and related rationality problems, and got several new results.
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Report
(5 results)
Research Products
(37 results)
